Category: Physics

Initial Reviews of my Book: Many Good, One Rather Inexplicable

September 17, 2025

So I’ve had some very nice reviews of my book, The Physics of Birds and Birding. I am very grateful for these, and they have been coming from birding organizations, birders, bloggers, and several ornithology journals. On a recent podcast, the American Birding Association had three reviewers good through their top five birding books of … More Initial Reviews of my Book: Many Good, One Rather Inexplicable

Errata, Some Fractals and Musings on Mandelbrot

May 15, 2025

I just found a small math error in my book. How annoying and frustrating. It is subtle and not something that most people would ever notice or care about, but before some astute, mathematically-inclined reader points it out, I want to provide the correction here. It doesn’t impact anything substantive I say in the book, … More Errata, Some Fractals and Musings on Mandelbrot

Anti-Reflection Coatings Part III: Oblique Incidence

December 24, 2024

Dealing with Non-normal Incidence In the previous post we developed the TMM for the special case of light incident in a direction perpendicular onto a multilayer coating. And as developed in the post before that, our treatment of the reflection and transmission coefficients required nothing more complicated than some commonsense assumptions about the behavior of … More Anti-Reflection Coatings Part III: Oblique Incidence

Anti-Reflection Coatings Part II: The Transfer Matrix Method

December 14, 2024

The Headache of Multiple Layers In the previous post we calculated the effect of a single dielectric layer placed between air and glass, and showed that with a judicious selection of index and thickness, it would serve as an anti-reflection coating that would pass 100% of the light at a nominal wavelength, and at least … More Anti-Reflection Coatings Part II: The Transfer Matrix Method

Anti-Reflection Coatings, Part I: Single Layer

December 11, 2024

Introduction It is well-known that the transmission of light through optical components such as lenses and prisms can be improved through the application of specialized dielectric coatings. We’ve come to take them for granted, and can easily forget that without them, the views through our instruments would be significantly dimmer. Any curious user of binoculars, … More Anti-Reflection Coatings, Part I: Single Layer

Technical References for Roof Prism Resolution Loss, Phase Coatings, and Related Topics

September 21, 2024

This page is meant to provide a list of references that are directly relevant (marked with a *) or in some cases marginally relevant to the topic of resolution loss in roof prisms and the so-called phase coatings used to mitigate the problem. If you know of any additional literature, please email me at hurbenm … More Technical References for Roof Prism Resolution Loss, Phase Coatings, and Related Topics

On the Passage of Linearly Polarized Light through an Uncoated Roof Prism

September 20, 2024

The famous Zeiss “paper” by Weruach and Dörband (translation attached below) on the development of phase coatings for roof prisms describes a simple test to determine if an optical instrument has coated prisms or not. They describe the use of two linear polarizers with the device placed in between; with phase coating present, one will … More On the Passage of Linearly Polarized Light through an Uncoated Roof Prism

The Physics of Roof Prism and Phase Coatings, Simplified: Polarization Effects

June 7, 2024

Many binoculars utilize roof prisms to keep the light along a single optical axis, making for a more compact shape. But the novel geometry of the prism’s reflecting surfaces creates a subtle interference effect which reduces the binocular’s resolution. The only way to mitigate this problem is to use specialized coatings on the roof surfaces. … More The Physics of Roof Prism and Phase Coatings, Simplified: Polarization Effects

How Electromagnetism Arises from Local Gauge Symmetry in Quantum Mechanics

November 27, 2023

This is one of the most beautiful results in all of physics, and I find it astonishing that at no point in my decade as a student was it presented or even mentioned. Typically, a formal introduction to the wavefunction and the Schrödinger equation is encountered at a senior undergraduate level. The fact that an … More How Electromagnetism Arises from Local Gauge Symmetry in Quantum Mechanics

The Physics of Parabolic Microphones: Frequency Dependence of Gain

October 13, 2023

Introduction Parabolic microphones are known for their extreme sensitivity, and the origin of their acuity isn’t difficult to guess. It is the most obvious thing about them, which can also make them a liability for field use, namely, their considerable size. Just as a large amount of weak light is captured by a telescope’s parabolic … More The Physics of Parabolic Microphones: Frequency Dependence of Gain

The Physics of Roof Prisms and Phase Coatings, Simplified: Part III

August 18, 2023

Diffraction patterns and resolution In the previous post we traced the passage of light through an Amici roof prism, which required decomposing vectors into components, accounting for phase shifts upon reflection, and then looking at how the waves will be recombined. We can now see that there will be an opportunity for interference effects to … More The Physics of Roof Prisms and Phase Coatings, Simplified: Part III

The Physics of Roof Prisms and Phase Coatings, Simplified: Part II

August 18, 2023

Phase shifts and interference The previous post introduced the topic of roof prism performance loss resulting from phase shifts that accompany total internal reflection (TIR). These shifts are endemic to TIR and to any device that employs it, including not only roof but Porro prisms. But in the latter case, the shifts have no deleterious … More The Physics of Roof Prisms and Phase Coatings, Simplified: Part II

The Physics of Roof Prisms and Phase Coatings, Simplified: Part I

August 18, 2023

Introduction Some time ago, I began a fruitless search for a detailed treatment of the performance losses endemic to roof prisms, and the so-called “phase coatings” that rectify the problem. Optics manufacturers tout the advantages of their proprietary coatings, but provide few specifics regarding the effect that their technology solves, or how their solution works. … More The Physics of Roof Prisms and Phase Coatings, Simplified: Part I

The Physics of Roof Prisms and Phase Coatings

July 22, 2023

I’ve written a technical article on the topic of why the roof prisms used in binoculars require specialized coatings in order to improve their performance. I was prompted to pull this together because I couldn’t find a single reference that traced through this interesting problem in a non-trivial way. The article includes a derivation of … More The Physics of Roof Prisms and Phase Coatings

I Went Parabolic and Now There is No Going Back

July 17, 2023

Edit: I recently added an article on the physics of parabolic microphone gain: LINK. When I was twelve I discovered astronomy and made my first optics purchase, a cheap, awful refracting telescope made by the K-mart subsidiary Focal. I knew I needed a more serious instrument, and soon became obsessed with something called the Dynascope … More I Went Parabolic and Now There is No Going Back

Making a More Convenient Shotgun Microphone Recording Rig

May 18, 2023

(Update: I changed microphones.) During the winter I made the jump to 32-bit audio recording with the Zoom F3 field recorder. I couple this with a Sennheiser MKH 416 shotgun microphone. I’d originally purchased the Rode NTG5, but it was horribly noisy. I soon learned that I wasn’t the only person that had trouble with … More Making a More Convenient Shotgun Microphone Recording Rig